Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... ·...
Transcript of Bottom-quark fragmentation and impact on the top mass ...nicotri/Bari_Xmas_Theory_Workshop... ·...
Bottom-quark fragmentation
and impact on the top mass reconstruction
Gennaro Corcella
INFN - Laboratori Nazionali di Frascati
1. Introduction
2. QCD calculations and Monte Carlo codes for b-fragmentation in top events
3. Hadronization models and fits to LEP and SLD data
4. B-hadron spectrum in top decay
5. Systematic error on the top mass measurement
6. Conclusions
Based on work by G.C., F.Mescia, V. Drollinger, A.D. Mitov, M. Cacciari, LEP, SLD, ATLAS and CMS top/heavy-quark
working groups
Work in progress with F.Mescia and K.Tywoniuk
– Typeset by FoilTEX – 1
Reliable description of multiple radiation in top production and decay and ofb-quark fragmentation is fundamental in the measurements of the top properties
Monte Carlo event generators (HERWIG/PYTHIA) widely used to simulate topproduction and decay and bottom-quark hadronization
LHC and Tevatron inclusive analyses (dilepton, lepton+jets and all-hadrons)propagate the uncertainty on b-fragmentation to the systematic error due tob-jet energy scale and b-tagging efficiency:
∆mt(bfrag) ≃ 250− 430 MeV ; ∆mt(tot) ≃ 920 MeV (TOPLHCWG)
J/ψ+ lepton final states (103/year in high-luminosity phase)
t→ bW ; b→ B → J/ψ X ; J/ψ → µ+µ− ; W → ℓνℓ
A. Kharchilava, PLB 476 (2000) 73, R. Chierici and A. Dierlamm, CMS Note 2006/058
mmax3ℓ = 0.56 mt − 25.3 GeV Systematics (theo + exp): ∆mt(syst) ≃ 1.47 GeV
b-fragmentation (PYTHIA+Peterson model): ∆mt(frag) ≃ 0.51 GeV
Several calculations and tools are available for bottom fragmentation in topdecays, but not unique strategy for the systematic error: comparing two tunedcodes/computations, one program varying fragmentation parameters, etc.
Top production and decays at hadron colliders, e.g. in qq̄ annihilation
Perturbative QCD allows one to calculate the parton-level (b-quark) spectrum
Phenomenological hadronization models are given in terms of non-perturbativefragmentation functions
σ(t→WB) = σ(t→Wb)⊗Dnp(b→ B)
Dnp(b→ B) contains parameters to be fitted to experimental data
Narrow-width approximation:
dσhaddxB
(t→ B) ≃dΓhad
dxB(t→ B) ;
dΓhad
dxB(t→ B) =
dΓpart
dxb(t→ b)⊗Dnp(b→ B)
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Top decay at NLO:
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t(q) → b(pb)W (pW )(
g(pg)
)
xb =1
1−m2W
/m2t
2pb·ptm2
t
1
Γ0
dΓ
dxb= δ(1− xb) +
αS(µ)
2π
[
Pqq(xb) lnm2
t
m2b
+A(xb)
]
+O
[(
mb
mt
)p]
Pqq(xb) = CF
(
1 + x2b1− xb
)
+
;
∫ 1
0
dxbf(xb)[g(xb)]+ =
∫ 1
0
dxb[f(xb)− f(1)]g(xb)
Mass logarithms and large-xb terms need resummation (soft/collinear radiation)
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b-quark energy spectrum in top decaymt=175 GeV, mb=5 GeV, mW=80.425 GeV, µF = µ = mt, µ0 = µ0F = mb, ΛMS
=200 GeV
Solid: soft and collinear resummation Dashes: only collinear resummation
Dots: massive NLO without resummation
Resummations in the NLL approximation:
Collinear: αS ln(m2t/m
2b), α
2S ln(m2
t/m2b), . . . α
nS lnn(m2
t/m2b), α
nS lnn−1(m2
t/m2b), . . .
Soft [1/(1− xb)+ → lnN ]: αS ln2N,αS lnN, . . . αnS lnn+1N,αn
S lnnN, . . .
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Monte Carlo generators for high-energy colliders
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Figure by Frank Krauss
Hard 2 → 2 subprocess: leading-order (LO) matrix element
Parton showers in the soft or collinear approximation
Matrix-element corrections for hard and large-angle parton radiation
Models for hadronization and underlying event
Parton shower algorithms
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θp(E)
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k(ω)
- p2(E2), z = ω/EdP = αS
2π P̂ (z)dz dQ2
Q2 ∆S(Q2max, Q
2)
Q2: ordering variable
∆S(Q2max, Q
2) Sudakov form factor: no radiation in [Q2, Q2max]
∆S(Q2max, Q
2) = exp
−αS
2π
∫ Q2max
Q2
dQ′2
Q′2
∫ zmax
zmin
dzP̂ (z)
HERWIG : Q2 = E2(1− cos θ) ≃ E2θ2/2 Soft approximation: angular ordering
PYTHIA (up to 6.2 version): Q2 = p2
It includes angular ordering only by an additional veto
PYTHIA 6.3 and 8: Q2 = k2T
Showers are equivalent to LO+LL resummation, with the inclusion of some NLLs(ΛMS → ΛMC = ΛMS exp(4Kβ0))
– Typeset by FoilTEX – 7
Hadronization: NP fragmentation functions and Monte Carlo models
DK(x, α) = (1 + α)(2 + α)x(1− x)α ; DP(x, ǫ) =NP
x [1− 1/x− ǫ/(1− x)]HERWIG: cluster model
Perturbative evolution ends at Q2 = Q20
Angular ordering ⇒ colour preconfinement
Forced gluon splitting (g → qq̄)
Colour-singlet clusters decay into the observed hadrons
PYTHIA: string model
q and q̄ move in opposite directions
The colour field collapses into a string with uniform energy density
qq̄ pairs are produced
The string breaks into the observed hadrons
Possible interface with NP fragmentation functions
Tuning involves hadronic and perturbative parameters: Q0, ΛMC, mg, etc. and relieson precise e+e− data (LHC data in future?)
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Bottom-quark fragmentation at the Z0 pole
0
100
200
300
0
100
200
300
0
100
200
300
0
100
200
0.2 0.6 1.0
SLD JETSET+Braaten et al. χ2= 83/16
JETSET+Collins, Spiller χ2= 103/16
JETSET+Lund χ2= 17/15
HERWIG χ2= 94/17
UCLA χ2= 25/17
JETSET+Peterson et al. χ2= 62/16
JETSET+Kartvelishvili et al. χ2= 34/16
JETSET+Bowler χ2= 17/15
En
trie
s
x Brec
x Brec
0.2 0.6 1.0
12-99 8515A1
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xwd
B
1/N
dN
/dxw
d
B
Data
Peterson
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xL
B
1/N
dN
/dxL B
Data
Peterson
ALEPH
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xwd
B
1/N
dN
/dxw
d
B
Data
Kartvelishvili
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xL
B
1/N
dN
/dxL B
Data
Kartvelishvili
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xwd
B
1/N
dN
/dxw
d
B
Data
Collins
0
1
2
3
0 0.2 0.4 0.6 0.8 1
xL
B
1/N
dN
/dxL B
Data
Collins
LEP tuning of PYTHIA+Peterson used in J/ψ + ℓ analysis
Best-fit parameters not the same, e.g. ǫb = 0.0033 (ALEPH), 0.0055 (SLD);αK = 11.9 (OPAL), 13.7 (ALEPH), 10.0 (SLD)
– Typeset by FoilTEX – 9
G. C. and V. Drollinger, NPB (2005): weakly-decaying B-hadron data from OPAL(mesons and baryons), ALEPH (only mesons) and SLD (mesons and baryons)
HERWIG PYTHIA
CLSMR(1) = 0.4 (0.0)CLSMR(2) = 0.3 (0.0) PARJ(41) = 0.85 (0.30)DECWT = 0.7 (1.0) PARJ(42) = 1.03 (0.58)CLPOW = 2.1 (2.0) PARJ(46) = 0.85 (1.00)
PSPLT(2) = 0.33 (1.00)
χ2/dof = 222.4/61 (739.4/61) χ2/dof = 45.7/61 (467.9/61)
Lund/Bowler fragmentation function (PYTHIA):
fB(z) ∝1
z1+brm2b
(1− z)a exp(−bm2T/z)
HERWIG tuned parameters describe hadron gaussian smearing (CLSMR),baryon/meson (CLPOW) and decuplet/octet (DECWT) ratios, mass spectrum ofb-like clusters (PSPLT)
Our PYTHIA tuning in ATLAS jet-energy measurement (EPJ C73 (2013) 2304) and asa cross-check for top analyses
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Comparing tuned HERWIG and PYTHIA and resummed calculations
NLO+NLL: M.Cacciari and S.Catani, NPB617 (2001) 253-290
Best fit (0.18 ≤ xB ≤ 0.94): α = 17.178± 0.303, χ2/dof = 46.2/53
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B-hadron spectrum in top decays:
Mild dependence on the top mass in both HERWIG and PYTHIA:
Discussion with CMS/ATLAS folks: xB hard to measure experimentally
– Typeset by FoilTEX – 12
B-lepton invariant mass according to tuned HERWIG and PYTHIA
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Linear fits to extract mt from mBℓ
HERWIG: 〈mBℓ〉H ≃ −25.31 GeV + 0.61 mt ; δ = 0.043 GeV
PYTHIA: 〈mBℓ〉P ≃ −24.11 GeV + 0.59 mt ; δ = 0.022 GeV
NLO: 〈mBℓ〉NLO ≃ −26.7 GeV + 0.60 mt ; δ = 0.004 GeV
S.Biswas, K.Melnikov and M.Schulze, JHEP 1008 (2010) 048: mBℓ at NLO
∆〈mBℓ〉H,P ≃ 1.2 GeV ; ∆〈mBℓ〉H,NLO ≃ 2.2 GeV ; ∆〈mBℓ〉P,NLO ≃ 1.1 GeV
NLO+showers for top decays or C++ codes may shed light on this discrepancy
– Typeset by FoilTEX – 14
HERWIG++ : improved fragmentation model and mass-dependent splitting functions
Pqq(z) = CF
[
1 + z2
1− z−
2m2
Q2z(1− z)
]
+
0 0.2 0.4 0.6 0.8 1
xE(B Hadrons)
-0.2-0.1
00.10.2
0
0.5
1
1.5
2
2.5
3
3.5no ME correctionδ = 1.7 GeVδ = 2.3 GeVδ = 3.2 GeVSLD 02
Left: HERWIG++ vs. SLD data on B-hadron energy fraction (δ: shower cutoff)
Right: tuning PYTHIA 8 (C++) to LEP and SLD data (K.Tywoniuk, preliminary)
– Typeset by FoilTEX – 15
Conclusions and outlook
Bottom fragmentation in top decays is a source of uncertainty on the measurementof the top properties in inclusive (b-tagging and b-energy scale) and exclusive analyses(J/ψ + ℓ)
LO+shower codes and NLO+NLL calculations for b-fragmentation, tuning hadronizationmodels to e+e− data
Predictions for top decays yielded by the different codes exhibit some discrepancies,mostly driven by unsatisfactory tunings
Preliminary results with object-oriented codes exhibit a better description of b-quarkfragmentation in e+e− collisions after the tuning
Perspectives:
Comparing tuned PYTHIA and HERWIG++ can be a valuable way to estimate b-hadronization systematics
Extending the analysis to NLO+showers tools (POWHEG and aMC@NLO with off-shelleffects) and ultimately NNLO calculations
Tuning fragmentation parameters directly to LHC data (tt̄, bb̄, Z/γ+ b) and comparisonwith e+e− fits to test factorization and quality of hadronization models
– Typeset by FoilTEX – 16